We present results of a signature-based search for new physics using a dijet plus missing transverse energy data sample collected in 2 fb-1 of p-pbar collisions at sqrt(s) = 1.96 TeV with the CDF II detector at the Fermilab Tevatron. We observe no significant event excess with respect to the standard model prediction and extract a 95% C.L. upper limit on the cross section times acceptance for a potential contribution from a non-standard model process. Based on this limit the mass of a first or